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<p>We are concerned with the problem of image segmentation, in which each pixel is assigned to one of a predefined finite number of labels. In Bayesian image analysis, this requires fusing together local predictions for the class labels with a prior model of label images. Following the work of, we consider the use of tree-structured belief networks (TSBNs) as prior models. The parameters in the TSBN are trained using a maximum-likelihood objective function with the EM algorithm and the resulting model is evaluated by calculating how efficiently it codes label images. A number of authors have used Gaussian mixture models to connect the label field to the image data. In this paper, we compare this approach to the scaled-likelihood method of where local predictions of pixel classification from neural networks are fused with the TSBN prior. Our results show a higher performance is obtained with the neural networks. We evaluate the classification results obtained and emphasize not only the <it>maximum a posteriori</it> segmentation, but also the uncertainty, as evidenced e.g., by the pixelwise posterior marginal entropies. We also investigate the use of <it>conditional</it> maximum-likelihood training for the TSBN and find that this gives rise to improved classification performance over the ML-trained TSBN.</p>
tree-structured belief network (TSBN), hierarchical modeling, Markov random field (MRF), neural network, scaled-likelihood method, conditional maximum-likelihood training, Gaussian mixture model, expectation-maximization (EM)
C.K.I. Williams, X. Feng, S.N. Felderhof, "Combining Belief Networks and Neural Networks for Scene Segmentation", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 24, no. , pp. 467-483, April 2002, doi:10.1109/34.993555
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